1. Field of the Invention
The present invention relates to a rotor angle detecting apparatus for detecting the rotor angle of a salient-pole DC brushless motor.
2. Description of the Related Art
In order to energize a DC brushless motor to obtain a desired torque, it is necessary to apply a voltage to the armatures in a suitable phase corresponding to the electric angle (hereinafter referred to as rotor angle) of the rotor which has magnetic poles. Therefore, the DC brushless motor generally has a position detecting sensor for detecting the rotor angle.
The DC brushless motor with the position detecting sensor is required to have a circuit combined with the motor driver unit for receiving a detected signal which is outputted from the position detecting sensor, and wires between the position detecting sensor and the motor driver unit. There have been proposed various attempts to detect the rotor angle without the position detecting sensor so as to reduce the cost of the DC brushless motor and the motor driver unit by dispensing with the position detecting sensor.
According to one of the proposals, the voltage applied to the armatures of the DC brushless motor is divided into voltages on two orthogonal axes, and when a high-frequency alternating voltage is applied to one axis, a current generated on the other axis in response to the application of the high-frequency alternating voltage is detected thereby to detect the rotor angle. However, this approach is disadvantageous in that it takes some time in an initial startup stage before the detected rotor angle reaches an actual rotor angle and it is difficult to correct the rotor angle.
Another proposed technique uses a data table containing stored data representative of a correlation between rotor angles and armature currents when two- or three-phase currents are passed through the armatures of the DC brushless motor. Detected currents flowing through the armatures are applied to the data table, and approximating calculations are made on data in the data table to detect a rotor angle. Problems of this process are that errors tend to occur due to the effect of motor parameters that differ from motor to motor and the approximating calculations.
Basic principles of the present invention will first be described below with reference to FIGS. 1(a) and 1(b) of the accompanying drawings. As shown in FIG. 1(a), a DC brushless motor 1 comprises a rotor 2 having field magnetic poles provided a permanent magnet and armatures 3, 4, 5 in three phases (U, V, W phases). When given alternating currents are supplied to the three-phase armatures 3, 4, 5, the rotor 2 is rotated by a revolving magnetic field which is produced as a combination of the magnetic fields generated by the armatures 3, 4, 5.
The revolving magnetic field needs to be generated in a direction depending on the angle xcex8 of the rotor 2 (in FIG. 1(a), the angle of the rotor 2 as measured clockwise from the U-phase armature 3, hereinafter referred to as xe2x80x9crotor angle xcex8xe2x80x9d). Therefore, it is required to detect the rotor angle xcex8 for the control of the DC brushless motor.
DC brushless motors generally have a position detecting sensor such as a resolver or the like for detecting the rotor angle xcex8. However, a rotor angle detecting apparatus for a DC brushless motor according to the present invention is capable of detecting the rotor angle xcex8 without a position detecting sensor and hence dispenses with the need for a position detecting sensor.
As shown in FIG. 1(a), with the salient-pole rotor 2 being used, the magnetic reluctance of a gap between the rotor 2 and the armatures 2, 3, 4 varies periodically as the rotor 2 rotates. When the rotor 2 makes one revolution, the magnetic reluctance varies in two cycles, i.e., when the rotor 2 makes one half of a revolution, the magnetic reluctance varies in one cycle. The magnetic reluctance is maximum when the rotor 2 is in a position {circumflex over (1)} and minimum when the rotor 2 is in a position {circumflex over (2)}.
The magnetic circuit of the DC brushless motor shown in FIG. 1(a) is schematically shown in FIG. 1(b) of the accompanying drawings. If it is assumed in FIG. 1(b) that the magnetic reluctance varies in a unit cosine-wave pattern and the average value thereof in one periodic cycle is 0.5, then the magnetic reluctances Ru, Rv, Rw in the respective phases U, V, W are expressed by the following equations (1) through (3):
Ru=1xe2x88x92cos 2xcex8xe2x80x83xe2x80x83(1)                     Rv        =                  1          -                      cos            ⁡                          (                                                2                  ⁢                  θ                                +                                                      2                    3                                    ⁢                  π                                            )                                                          (        2        )                                Rw        =                  1          -                      cos            ⁡                          (                                                2                  ⁢                  θ                                -                                                      2                    3                                    ⁢                  π                                            )                                                          (        3        )            
At this time, the magnetic reluctance Rtu of the gap as seen from the U phase can be determined according to the following equation (4):                                                         Rgu              =                              Ru                +                                                      Rv                    ·                    Rw                                                        Rv                    +                    Rw                                                                                                                          =                              1                +                                  cos                  ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                                      xe2x80x83                                    ⁢                  θ                                +                                                                                        =                                                1                  +                                      cos                    ⁡                                          (                                                                        2                          ⁢                          θ                                                -                                                                              2                            3                                                    ⁢                          π                                                                    )                                                        +                                      cos                    ⁡                                          (                                                                        2                          ⁢                          θ                                                +                                                                              2                            3                                                    ⁢                          π                                                                    )                                                        +                                                            cos                      ⁡                                              (                                                                              2                            ⁢                            θ                                                    -                                                                                    2                              3                                                        ⁢                            π                                                                          )                                                              ·                                          cos                      ⁡                                              (                                                                              2                            ⁢                            θ                                                    +                                                                                    2                              3                                                        ⁢                            π                                                                          )                                                                                                              2                  +                                      cos                    ⁡                                          (                                                                        2                          ⁢                          θ                                                -                                                                              2                            3                                                    ⁢                          π                                                                    )                                                        +                                      cos                    ⁡                                          (                                                                        2                          ⁢                          θ                                                +                                                                              2                            3                                                    ⁢                          π                                                                    )                                                                                                                                              =                              1                +                                  cos                  ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                                      xe2x80x83                                    ⁢                  θ                                +                                                      1                    -                                          cos                      ⁢                                              xe2x80x83                                            ⁢                      2                      ⁢                      θ                                        +                                                                  1                        2                                            ⁢                                              (                                                                              cos                            ⁢                                                          xe2x80x83                                                        ⁢                            4                            ⁢                            θ                                                    +                                                      cos                            ⁢                                                          2                              3                                                        ⁢                            π                                                                          )                                                                                                  2                    -                                          cos                      ⁢                                              xe2x80x83                                            ⁢                      2                      ⁢                      θ                                                                                                                                              =                                                8                  -                                      cos                    ⁢                                          2                      3                                        ⁢                    π                                                                    4                  -                                      2                    ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                    2                    ⁢                    θ                                                                                                          (        4        )            
Therefore, if it is assumed that the U-phase comprises a unit winding, then the self-inductance of the U phase can be determined according to the following equation (5):                     Lu        =                              1            Rgu                    =                                    4              -                              2                ⁢                cos                ⁢                                  xe2x80x83                                ⁢                2                ⁢                θ                                                    8              -                              cos                ⁢                                  2                  3                                ⁢                π                                                                        (        5        )            
The mutual inductance Muw between the U and W phases and the mutual inductance Muv between the U and V phases can be determined according to the following equations (6), (7), respectively, because of the arrangement of the magnetic circuit:                     Muw        =                                            -                              Rw                                  Rv                  +                  Rw                                                      ⁢            Lu                    =                      -                                          2                +                                  2                  ⁢                                      cos                    ⁡                                          (                                                                        2                          ⁢                          θ                                                +                                                                              2                            3                                                    ⁢                          π                                                                    )                                                                                                  8                -                                  cos                  ⁢                                      xe2x80x83                                    ⁢                                      2                    3                                    ⁢                  π                                                                                        (        6        )                                Muv        =                                            -                              Rv                                  Rv                  +                  Rw                                                      ⁢            Lu                    =                      -                                          2                +                                  2                  ⁢                                      cos                    ⁡                                          (                                                                        2                          ⁢                          θ                                                -                                                                              2                            3                                                    ⁢                          π                                                                    )                                                                                                  8                -                                  cos                  ⁢                                      xe2x80x83                                    ⁢                                      2                    3                                    ⁢                  π                                                                                        (        7        )            
The self-inductances and the mutual inductances of the V and W phases can similarly be determined. If the DC component of the self-inductance of each phase is represented by 1, a variation of the DC component 1 by xcex941, and the DC component of the mutual inductance between each phase pair by m, then the voltage equation of the DC brushless motor with the salient-pole rotor is given as follows:                               [                                                    VU                                                                    VV                                                                    VW                                              ]                =                              r            ⁡                          [                                                                    Iu                                                                                        Iv                                                                                        Iw                                                              ]                                +                                                                                          xe2x80x83                                    ⅆ                                                  ⅆ                  t                                            ⁡                              [                                                                                                    1                        -                        Δ1cos2θ                                                                                                            m                        -                                                  Δ1cos                          ⁡                                                      (                                                                                          2                                ⁢                                θ                                                            -                                                                                                2                                  3                                                                ⁢                                π                                                                                      )                                                                                                                                                              m                        -                                                  Δ1cos                          ⁡                                                      (                                                                                          2                                ⁢                                θ                                                            +                                                                                                2                                  3                                                                ⁢                                π                                                                                      )                                                                                                                                                                                                  m                        -                                                  Δ1cos                          ⁡                                                      (                                                                                          2                                ⁢                                θ                                                            -                                                                                                2                                  3                                                                ⁢                                π                                                                                      )                                                                                                                                                              1                        -                                                  Δ1cos                          ⁡                                                      (                                                                                          2                                ⁢                                θ                                                            +                                                                                                2                                  3                                                                ⁢                                π                                                                                      )                                                                                                                                                              m                        -                        Δ1cos2θ                                                                                                                                                m                        -                                                  Δ1cos                          ⁡                                                      (                                                                                          2                                ⁢                                θ                                                            +                                                                                                2                                  3                                                                ⁢                                π                                                                                      )                                                                                                                                                              m                        -                        Δ1cos2θ                                                                                                            1                        -                                                  Δ1cos                          ⁡                                                      (                                                                                          2                                ⁢                                θ                                                            -                                                                                                2                                  3                                                                ⁢                                π                                                                                      )                                                                                                                                              ]                                      ⁢                          xe2x80x83                        [                                                            Iu                                                                              Iv                                                                              Iw                                                      ]                    +                                    ω              m                        ⁢            Ke            ⁢                          ⌈                                                                                          sin                      ⁢                                              xe2x80x83                                            ⁢                      θ                                                                                                                                  sin                      ⁡                                              (                                                  θ                          -                                                                                    2                              3                                                        ⁢                            π                                                                          )                                                                                                                                                        sin                      ⁡                                              (                                                  θ                          -                                                                                    4                              3                                                        ⁢                            π                                                                          )                                                                                                        ⌉                                                          (        8        )            
where VU, VV, VW represent respective voltages applied to the U-, V-, W-phase armatures, Iu, Iv, Iw represent respective currents flowing through the U-, V-, W-phase armatures, r represents the electric resistance of each of the U-, V-, W-phase armatures, xcfx89m represents the electric angular velocity of the rotor 2, and Ke represents an induced voltage constant.
If the electric angular velocity xcfx89m is substantially 0, any effect of changes in the induced voltage and the angular velocity of the rotor 2 are small, and the voltage drop due to the resistance r is negligibly small in level, then the above equation (8) can be regarded and handled as the following equation (9):                               [                                                    VU                                                                    VV                                                                    VW                                              ]                ≈                  "AutoLeftMatch"                                    [                                                                                          1                      -                      Δ1cos2θ                                                                                                  m                      -                                              Δ1cos                        ⁡                                                  (                                                                                    2                              ⁢                              θ                                                        -                                                                                          2                                3                                                            ⁢                              π                                                                                )                                                                                                                                                m                      -                                              Δ1cos                        ⁡                                                  (                                                                                    2                              ⁢                              θ                                                        +                                                                                          2                                3                                                            ⁢                              π                                                                                )                                                                                                                                                                                m                      -                                              Δ1cos                        ⁡                                                  (                                                                                    2                              ⁢                              θ                                                        -                                                                                          2                                3                                                            ⁢                              π                                                                                )                                                                                                                                                1                      -                                              Δ1cos                        ⁡                                                  (                                                                                    2                              ⁢                              θ                                                        +                                                                                          2                                3                                                            ⁢                              π                                                                                )                                                                                                                                                m                      -                      Δ1cos2θ                                                                                                                                  m                      -                                              Δ1cos                        ⁡                                                  (                                                                                    2                              ⁢                              θ                                                        +                                                                                          2                                3                                                            ⁢                              π                                                                                )                                                                                                                                                m                      -                      Δ1cos2θ                                                                                                  1                      -                                              Δ1cos                        ⁡                                                  (                                                                                    2                              ⁢                              θ                                                        -                                                                                          2                                3                                                            ⁢                              π                                                                                )                                                                                                                                ]                        ⁢                                                                                xe2x80x83                                    ⅆ                                                  ⅆ                  t                                            ⁡                              [                                                                            Iu                                                                                                  Iv                                                                                                  Iw                                                                      ]                                                                        (        9        )            
In view of the fact that the sum of the currents flowing in the respective phases is zero, the equation (9) can be modified in terms of Iu, Iv, Iw as indicated by the following equation (10):                                                                         xe2x80x83                            ⅆ                                      ⅆ              t                                ⁡                      [                                                            Iu                                                                              Iv                                                                              Iw                                                      ]                          =                  K          ⁢                                    ⌈                                                                                          1                      -                      m                      +                      Δ1cos2θ                                                                                                  Δ1cos                      ⁡                                              (                                                                              2                            ⁢                            θ                                                    -                                                                                    2                              3                                                        ⁢                            π                                                                          )                                                                                                                        Δ1cos                      ⁡                                              (                                                                              2                            ⁢                            θ                                                    +                                                                                    2                              3                                                        ⁢                            π                                                                          )                                                                                                                                                        Δ1cos                      ⁡                                              (                                                                              2                            ⁢                            θ                                                    -                                                                                    2                              3                                                        ⁢                            π                                                                          )                                                                                                                        1                      -                      m                      +                                              Δ1cos                        ⁡                                                  (                                                                                    2                              ⁢                              θ                                                        +                                                                                          2                                3                                                            ⁢                              π                                                                                )                                                                                                                          Δ1cos2θ                                                                                                              Δ1cos                      ⁡                                              (                                                                              2                            ⁢                            θ                                                    +                                                                                    2                              3                                                        ⁢                            π                                                                          )                                                                                                  Δ1cos2θ                                                                              1                      -                      m                      +                                              Δ1cos                        ⁡                                                  (                                                                                    2                              ⁢                              θ                                                        -                                                                                          2                                3                                                            ⁢                              π                                                                                )                                                                                                                                ⌉                        ⁢                          xe2x80x83                        [                                                            VU                                                                              VV                                                                              VW                                                      ]                                              (        10        )            
where the calculating gain K is represented by the following equation (11):                     K        =                  1                                    2              ⁢                                                (                                      1                    -                    m                                    )                                ·                1                                      -                                          Δ1                2                            ⁡                              (                                                      3                    2                                    +                                      3                    ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                                          2                      3                                        ⁢                    π                                                  )                                                                        (        11        )            
When a high-frequency voltage imposer 21 (see FIG. 2 of the accompanying drawings) imposes high-frequency voltages vv, vu, vw, expressed by the following equation (12), on respective control voltage command values VU_c, VV_c, VW_c applied to the U-, V-, W-phase armatures, the current Iu flowing through the U-phase armature varies by a quantity represented by the following equation (13):                                           [                                                            vu                                                                              vv                                                                              vw                                                      ]                    =                      ω            ⁡                          [                                                                                          sin                      ⁢                                              xe2x80x83                                            ⁢                      ω                                                                                                                                  sin                      ⁡                                              (                                                                              ω                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    -                                                                                    2                              3                                                        ⁢                            π                                                                          )                                                                                                                                                        sin                      ⁡                                              (                                                                              ω                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    -                                                                                    4                              3                                                        ⁢                            π                                                                          )                                                                                                        ]                                      ⁢                  xe2x80x83                                    (        12        )                                                                                                      ⅆ                                      ⅆ                    t                                                  ⁢                Iu                            =                              xe2x80x83                            ⁢                              ω                ⁢                                  xe2x80x83                                ⁢                                  K                  [                                                                                    (                                                  1                          -                          m                                                )                                            ⁢                      sin                      ⁢                                              xe2x80x83                                            ⁢                      ω                      ⁢                                              xe2x80x83                                            ⁢                      t                                        +                                          Δ1                      ⁢                                              {                                                                              cos                            ⁢                                                          xe2x80x83                                                        ⁢                            2                            ⁢                            θsinω                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    +                                                ⁢                                                  xe2x80x83                                                                                                                                                                                                                              xe2x80x83                                ⁢                                                      cos                    ⁢                                          (                                                                        2                          ⁢                          θ                                                -                                                                              2                            3                                                    ⁢                          π                                                                    )                                        ⁢                                          sin                      ⁡                                              (                                                                              ω                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    -                                                                                    2                              3                                                        ⁢                            π                                                                          )                                                                              ⁢                                      xe2x80x83                                    +                                      cos                    ⁢                                          (                                                                        2                          ⁢                          θ                                                +                                                                              2                            3                                                    ⁢                          π                                                                    )                                        ⁢                                          sin                      ⁡                                              (                                                                              ω                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    +                                                                                    2                              3                                                        ⁢                            π                                                                          )                                                                                            }                            ]                                                                          =                              xe2x80x83                            ⁢                              ω                ⁢                                  xe2x80x83                                ⁢                                  K                  ⁡                                      [                                                                                            (                                                      1                            -                            m                                                    )                                                ⁢                        sin                        ⁢                                                  xe2x80x83                                                ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                        t                                            -                                                                                                    3                            ⁢                            Δ1                                                    2                                                ⁢                                                  sin                          ⁡                                                      (                                                                                          2                                ⁢                                θ                                                            -                                                              ω                                ⁢                                                                  xe2x80x83                                                                ⁢                                t                                                                                      )                                                                                                                ]                                                                                                          (        13        )            
where xcfx89 represents the electric angular velocity of the high-frequency voltages vv, vu, vw.
The current Iw flowing through the W-phase armature varies by a quantity represented by the following equation (14):                                                         ⅆ                              ⅆ                t                                      ⁢            Iw                    =                                    ω              ⁢                              xe2x80x83                            ⁢                              K                ⁡                                  [                                                            (                                              1                        -                        m                                            )                                        ⁢                    sin                    ⁢                                          xe2x80x83                                        ⁢                                          (                                                                        ω                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                +                                                                              2                            3                                                    ⁢                          π                                                                    )                                        ⁢                    Δ1                    ⁢                                          {                                                                        cos                          ⁢                                                      xe2x80x83                                                    ⁢                                                      (                                                                                          2                                ⁢                                θ                                                            +                                                                                                2                                  3                                                                ⁢                                π                                                                                      )                                                    ⁢                          sin                          ⁢                                                      xe2x80x83                                                    ⁢                          ω                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                +                                                  cos                          ⁢                                                      xe2x80x83                                                    ⁢                          2                          ⁢                                                      θsin                            ⁡                                                          (                                                                                                ω                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  t                                                                -                                                                                                      2                                    3                                                                    ⁢                                  π                                                                                            )                                                                                                      +                                                                              cos                            ⁡                                                          (                                                                                                2                                  ⁢                                  θ                                                                -                                                                                                      2                                    3                                                                    ⁢                                  π                                                                                            )                                                                                ⁢                                                      sin                            ⁡                                                          (                                                                                                ω                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  t                                                                +                                                                                                      2                                    3                                                                    ⁢                                  π                                                                                            )                                                                                                                          }                                                        ]                                                      ⁢                          
                        ⁢                          xe2x80x83                        =                          ω              ⁢                              xe2x80x83                            ⁢                              K                ⁡                                  [                                                                                    (                                                  1                          -                          m                                                )                                            ⁢                      sin                      ⁢                                              xe2x80x83                                            ⁢                                              (                                                                              ω                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    +                                                                                    2                              3                                                        ⁢                            π                                                                          )                                                              -                                                                                            3                          ⁢                          Δ1                                                2                                            ⁢                                              sin                        ⁡                                                  (                                                                                    2                              ⁢                              θ                                                        -                                                          ω                              ⁢                                                              xe2x80x83                                                            ⁢                              t                                                        +                                                                                          2                                3                                                            ⁢                              π                                                                                )                                                                                                      ]                                                                    ⁢                  xe2x80x83                                    (        14        )            
By integrating the equations (13), (14) with respect to time t, the currents Iu, Iw can be determined by the following equations (15), (16):                               I          ⁢                      xe2x80x83                    ⁢          u                =                  K          ⁡                      [                                                            -                                      (                                          1                      -                      m                                        )                                                  ⁢                cos                ⁢                                  xe2x80x83                                ⁢                ω                ⁢                                  xe2x80x83                                ⁢                t                            -                                                                    3                    ⁢                    Δ1                                    2                                ⁢                                  cos                  ⁡                                      (                                                                  2                        ⁢                        θ                                            -                                              ω                        ⁢                                                  xe2x80x83                                                ⁢                        t                                                              )                                                                        ]                                              (        15        )                                          I          ⁢                      xe2x80x83                    ⁢          w                =                  K          ⁡                      [                                                            -                                      (                                          1                      -                      m                                        )                                                  ⁢                cos                ⁢                                  xe2x80x83                                ⁢                                  (                                                            ω                      ⁢                                              xe2x80x83                                            ⁢                      t                                        +                                                                  2                        3                                            ⁢                      π                                                        )                                            -                                                                    3                    ⁢                    Δ1                                    2                                ⁢                                  cos                  ⁡                                      (                                                                  2                        ⁢                        θ                                            -                                              ω                        ⁢                                                  xe2x80x83                                                ⁢                        t                                            +                                                                        2                          3                                                ⁢                        π                                                              )                                                                        ]                                              (        16        )            
The equations (15), (16) show that the currents Iu, Iw vary depending on the angular velocity xcfx89 of the added high-frequency voltages vu, vv, vw and the rotor angle xcex8. Therefore, it is proposed to detect the rotor angle xcex8 by detecting the currents Iu, Iw which flow when the high-frequency voltages vu, vv, vw with the known angular velocity xcfx89 are added.
The present invention will be described below on the basis of the principles described above. According to the present invention, there is provided a rotor angle apparatus for a DC brushless motor, comprising voltage applying means for applying drive voltages to three-phase armatures of a salient-pole DC brushless motor, high-frequency voltage imposing means for imposing high-frequency voltages to the drive voltages, respectively, first current detecting means for detecting a current flowing through a first-phase armature among the three-phase armatures, second current detecting means for detecting a current flowing through a second-phase armature among the three-phase armatures, reference value extracting means for extracting a sine reference value depending on a sine value which is twice the rotor angle of the DC brushless motor and a cosine reference value depending on a cosine value which is twice the rotor angle of the DC brushless motor, using a first current value detected by the first current detecting means and a second current value detected by the second current detecting means when the high-frequency voltages are imposed on the drive voltages by the high-frequency voltage imposing means, and high-frequency components depending on the high-frequency voltages, and rotor angle calculating means for calculating the rotor angle of the DC brushless motor from the sine reference value and the cosine reference value.
While the high-frequency voltage imposing means imposes the high-frequency voltages on the drive voltages applied to the armatures of the DC brushless motor and the first current detecting means and the second current detecting means detect the first current value and the second current value, respectively, the reference value extracting means can extract the sine reference value and the cosine reference value according to the equations (15), (16). The rotor angle calculating means can directly calculate the rotor angle of the DC brushless motor from the sine reference value and the cosine reference value which are extracted by the reference value extracting means. The rotor angle detecting apparatus according to the present invention has a better initial follow-up capability than conventional apparatus, and can detect the rotor angle accurately without being affected by the motor parameters.
The reference value extracting means effects an integrating process or a low-pass filtering process on the high-frequency components to extract the sine reference value and the cosine reference value.
By effecting the integrating process or the low-pass filtering process, the reference value extracting means can fix the high-frequency components which tend to vary with time and extract the sine reference value and the cosine reference value.
The rotor angle calculating means calculates phase difference data representing a phase difference (xcex8xe2x88x92{circumflex over (xcex8)}) between an estimated value ({circumflex over (xcex8)}) and an actual value (xcex8) of the rotor angle of the DC brushless motor, using the sine reference value and the cosine reference value, and calculates the rotor angle according to follow-up calculations using an observer which is constructed to eliminate the phase difference (xcex8xe2x88x92{circumflex over (xcex8)}) represented by the phase difference data.
The rotor angle calculating means can calculate the rotor angle from the sine reference value and the cosine reference value by using the observer.
Using Iu, Iw determined by the above equations (15), (16), the relationship of the following equation (17) is obtained:                               xe2x80x83                ⁢                                                                                                                                                cos                        ⁡                                                  (                                                                                    ω                              ⁢                                                              xe2x80x83                                                            ⁢                              t                                                        +                                                                                          2                                3                                                            ⁢                              π                                                                                )                                                                    ·                      I                                        ⁢                                          xe2x80x83                                        ⁢                    u                                    -                                      cos                    ⁢                                          xe2x80x83                                        ⁢                    ω                    ⁢                                          xe2x80x83                                        ⁢                                          t                      ·                      I                                        ⁢                                          xe2x80x83                                        ⁢                    w                                                  =                                  xe2x80x83                                ⁢                                  K                  [                                                                                    -                                                  (                                                      1                            -                            m                                                    )                                                                    ⁢                                              cos                        ⁡                                                  (                                                      ωt                            +                                                                                          2                                3                                                            ⁢                              π                                                                                )                                                                    ⁢                      cos                      ⁢                                              xe2x80x83                                            ⁢                      ω                      ⁢                                              xe2x80x83                                            ⁢                      t                                        -                                                                                            3                          ⁢                          Δ1                                                2                                            ⁢                                              cos                        ⁡                                                  (                                                      ωt                            +                                                                                          2                                3                                                            ⁢                              π                                                                                )                                                                    ⁢                      cos                      ⁢                                              (                                                                              2                            ⁢                            θ                                                    -                                                      ω                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                                          )                                                              +                                                                                                                                            xe2x80x83                                ⁢                                                                            (                                              1                        -                        m                                            )                                        ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                    ω                    ⁢                                          xe2x80x83                                        ⁢                    t                    ⁢                                          xe2x80x83                                        ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                                          (                                              ωt                        +                                                                              2                            3                                                    ⁢                          π                                                                    )                                                        +                                                                                    3                        ⁢                        Δ1                                            2                                        ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                    ω                    ⁢                                          xe2x80x83                                        ⁢                    t                    ⁢                                          xe2x80x83                                        ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                                          (                                                                        2                          ⁢                          θ                                                -                                                  ω                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                +                                                                              2                            3                                                    ⁢                          π                                                                    )                                                                      ⁢                                  
                                ⁢                                  xe2x80x83                                                                                                        =                                  xe2x80x83                                ⁢                                  K                  ⁢                                                                                    3                        ⁢                        Δ1                                            2                                        ⁡                                          [                                                                        -                                                      cos                            ⁡                                                          (                                                                                                2                                  ⁢                                  ω                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  t                                                                -                                                                  2                                  ⁢                                  θ                                                                -                                                                                                      2                                    3                                                                    ⁢                                  π                                                                                            )                                                                                                      +                                                  cos                          ⁡                                                      (                                                                                          2                                ⁢                                ω                                ⁢                                                                  xe2x80x83                                                                ⁢                                t                                                            -                                                              2                                ⁢                                θ                                                            -                                                                                                2                                  3                                                                ⁢                                π                                                                                      )                                                                                              ]                                                                                                                                              =                                  xe2x80x83                                ⁢                                                      -                    K                                    ⁢                                                                                    3                        ⁢                                                  3                                                ⁢                        Δ1                                            2                                        ⁡                                          [                                              sin                        ⁡                                                  (                                                                                    2                              ⁢                              ω                              ⁢                                                              xe2x80x83                                                            ⁢                              t                                                        -                                                          2                              ⁢                              θ                                                                                )                                                                    ]                                                                                                                              (        17        )            
Since the currents flowing through the U- and W-phase armatures generally contain a DC component, the current Iu flowing through the U-phase armature and the current Iw flowing through the W-phase armature are rewritten as the following equations (18), (19):                               I          ⁢                      xe2x80x83                    ⁢          u                =                              K            ⁡                          [                                                                    -                                          (                                              1                        -                        m                                            )                                                        ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                  ω                  ⁢                                      xe2x80x83                                    ⁢                  t                                -                                                                            3                      ⁢                      Δ1                                        2                                    ⁢                                      cos                    ⁡                                          (                                                                        2                          ⁢                          θ                                                -                                                  ω                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                                    )                                                                                  ]                                +                      I            ⁢                          xe2x80x83                        ⁢            u            ⁢                          xe2x80x83                        ⁢            d            ⁢                          xe2x80x83                        ⁢            c                                              (        18        )            
where Iudc: the DC component of the current flowing through the U-phase armature.                               I          ⁢                      xe2x80x83                    ⁢          w                =                              K            ⁡                          [                                                                    -                                          (                                              1                        -                        m                                            )                                                        ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                                      (                                                                  ω                        ⁢                                                  xe2x80x83                                                ⁢                        t                                            +                                                                        2                          3                                                ⁢                        π                                                              )                                                  -                                                                            3                      ⁢                      Δ1                                        2                                    ⁢                                      cos                    ⁡                                          (                                                                        2                          ⁢                          θ                                                -                                                  ω                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                +                                                                              2                            3                                                    ⁢                          π                                                                    )                                                                                  ]                                +                      I            ⁢                          xe2x80x83                        ⁢            w            ⁢                          xe2x80x83                        ⁢            d            ⁢                          xe2x80x83                        ⁢            c                                              (        19        )            
where Iwdc: the DC component of the current flowing through the W-phase armature.
From the relationship of the equation (17) and the following equation (20), a sine reference value Vs and a cosine reference value Vc which are twice (2xcex8) the rotor angle xcex8 can be calculated respectively by the following equations (21), (22), the currents Iu, Iw containing the DC components according to the equations (18), (19) and high-frequency components depending on the imposed high-frequency voltages:
sin (2xcfx89txe2x88x922xcex8)=sin 2xcfx89t cos 2xcex8xe2x88x92cos 2xcfx89t sin 2xcex8xe2x80x83xe2x80x83(20)                                                                         V                ⁢                                  xe2x80x83                                ⁢                s                            =                              xe2x80x83                            ⁢                                                ∫                  0                                                            2                      ⁢                      π                                        ω                                                  ⁢                                                      (                                                                  cos                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                        t                        ⁢                                                  xe2x80x83                                                ⁢                                                                              cos                            ⁡                                                          (                                                              ωt                                +                                                                                                      2                                    3                                                                    ⁢                                  π                                                                                            )                                                                                ·                          I                                                ⁢                                                  xe2x80x83                                                ⁢                        u                                            -                                              cos                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                        t                        ⁢                                                  xe2x80x83                                                ⁢                        cos                        ⁢                                                  xe2x80x83                                                ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                                                  t                          ·                          I                                                ⁢                                                  xe2x80x83                                                ⁢                        w                                                              )                                    ⁢                                      xe2x80x83                                    ⁢                                      ⅆ                    t                                                                                                                          =                              xe2x80x83                            ⁢                                                                    -                    K                                    ⁢                                                            3                      ⁢                                              3                                            ⁢                      Δ1                                        2                                    ⁢                                                            ∫                      0                                                                        2                          ⁢                          π                                                ω                                                              ⁢                                          cos                      ⁢                                              xe2x80x83                                            ⁢                      2                      ⁢                      ω                      ⁢                                              xe2x80x83                                            ⁢                      t                      ⁢                                              xe2x80x83                                            ⁢                                              sin                        ⁡                                                  (                                                                                    2                              ⁢                              ω                              ⁢                                                              xe2x80x83                                                            ⁢                              t                                                        -                                                          2                              ⁢                              θ                                                                                )                                                                    ⁢                                              ⅆ                        t                                                                                            +                                                                                                        xe2x80x83                            ⁢                                                ∫                  0                                                            2                      ⁢                      π                                        ω                                                  ⁢                                                      (                                                                  cos                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                                                  t                          ·                                                      xe2x80x83                                                    ⁢                                                      cos                            ⁡                                                          (                                                              ωt                                +                                                                                                      2                                    3                                                                    ⁢                                  π                                                                                            )                                                                                ·                          I                                                ⁢                                                  xe2x80x83                                                ⁢                        u                        ⁢                                                  xe2x80x83                                                ⁢                        d                        ⁢                                                  xe2x80x83                                                ⁢                        c                                            -                                              cos                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                                                  t                          ·                                                      xe2x80x83                                                    ⁢                          cos                                                ⁢                                                  xe2x80x83                                                ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                                                  t                          ·                          I                                                ⁢                                                  xe2x80x83                                                ⁢                        w                        ⁢                                                  xe2x80x83                                                ⁢                        d                        ⁢                                                  xe2x80x83                                                ⁢                        c                                                              )                                    ⁢                                      xe2x80x83                                    ⁢                                      ⅆ                    t                                                                                                                          =                              xe2x80x83                            ⁢                                                                    -                    K                                    ⁢                                                            3                      ⁢                                              3                                            ⁢                      Δ1                                        2                                    ⁢                                                            ∫                      0                                                                        2                          ⁢                          π                                                ω                                                              ⁢                                                                  (                                                                                                                                            sin                                ⁢                                                                  xe2x80x83                                                                ⁢                                4                                ⁢                                ω                                ⁢                                                                  xe2x80x83                                                                ⁢                                t                                                            2                                                        ⁢                            cos                            ⁢                                                          xe2x80x83                                                        ⁢                            2                            ⁢                            θ                                                    -                                                                                                                    1                                +                                                                  cos                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  4                                  ⁢                                  ω                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  t                                                                                            2                                                        ⁢                            sin                            ⁢                                                          xe2x80x83                                                        ⁢                            2                            ⁢                            θ                                                                          )                                            ⁢                                              ⅆ                        t                                                                                            +                                                                                                        xe2x80x83                            ⁢                                                ∫                  0                                                            2                      ⁢                      π                                        ω                                                  ⁢                                  (                                                                                                                                          cos                            ⁡                                                          (                                                                                                3                                  ⁢                                  ω                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  t                                                                +                                                                                                      2                                    3                                                                    ⁢                                  π                                                                                            )                                                                                +                                                      cos                            ⁡                                                          (                                                                                                ω                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  t                                                                -                                                                                                      2                                    3                                                                    ⁢                                  π                                                                                            )                                                                                                      2                                            ⁢                      I                      ⁢                                              xe2x80x83                                            ⁢                      u                      ⁢                                              xe2x80x83                                            ⁢                      d                      ⁢                                              xe2x80x83                                            ⁢                      c                                        -                                                                                                                                                            xe2x80x83                                ⁢                                                                                                                              cos                          ⁢                                                      xe2x80x83                                                    ⁢                          3                          ⁢                                                      xe2x80x83                                                    ⁢                          ω                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                +                                                  cos                          ⁢                                                      xe2x80x83                                                    ⁢                          ω                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                                    2                                        ⁢                    I                    ⁢                                          xe2x80x83                                        ⁢                    w                    ⁢                                          xe2x80x83                                        ⁢                    d                    ⁢                                          xe2x80x83                                        ⁢                    c                                    )                                            ⁢                              ⅆ                t                                                                                        =                              xe2x80x83                            ⁢                                                                    2                    ⁢                    π                                    ω                                ⁢                K                ⁢                                                      3                    ⁢                                          3                                        ⁢                    Δ1                                    4                                ⁢                sin                ⁢                                  xe2x80x83                                ⁢                2                ⁢                θ                                                                        (        21        )                                                                    Vc              =                              xe2x80x83                            ⁢                                                ∫                  0                                                            2                      ⁢                      π                                        ω                                                  ⁢                                                      (                                                                  sin                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                        t                        ⁢                                                  xe2x80x83                                                ⁢                                                                              cos                            ⁡                                                          (                                                              ωt                                +                                                                                                      2                                    3                                                                    ⁢                                  π                                                                                            )                                                                                ·                          I                                                ⁢                                                  xe2x80x83                                                ⁢                        u                                            -                                              sin                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                        t                        ⁢                                                  xe2x80x83                                                ⁢                        cos                        ⁢                                                  xe2x80x83                                                ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                                                  t                          ·                          I                                                ⁢                                                  xe2x80x83                                                ⁢                        w                                                              )                                    ⁢                                      xe2x80x83                                    ⁢                                      ⅆ                    t                                                                                                                          =                              xe2x80x83                            ⁢                                                K                  ⁢                                                            3                      ⁢                                              3                                            ⁢                      Δ1                                        2                                    ⁢                                                            ∫                      0                                                                        2                          ⁢                          π                                                ω                                                              ⁢                                          sin                      ⁢                                              xe2x80x83                                            ⁢                      2                      ⁢                      ω                      ⁢                                              xe2x80x83                                            ⁢                      t                      ⁢                                              xe2x80x83                                            ⁢                                              sin                        ⁡                                                  (                                                                                    2                              ⁢                              ω                              ⁢                                                              xe2x80x83                                                            ⁢                              t                                                        -                                                          2                              ⁢                              θ                                                                                )                                                                    ⁢                                              ⅆ                        t                                                                                            +                                                                                                        xe2x80x83                            ⁢                                                ∫                  0                                                            2                      ⁢                      π                                        ω                                                  ⁢                                                      (                                                                  sin                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                                                  t                          ·                                                      xe2x80x83                                                    ⁢                                                      cos                            ⁡                                                          (                                                              ωt                                +                                                                                                      2                                    3                                                                    ⁢                                  π                                                                                            )                                                                                ·                          I                                                ⁢                                                  xe2x80x83                                                ⁢                        u                        ⁢                                                  xe2x80x83                                                ⁢                        d                        ⁢                                                  xe2x80x83                                                ⁢                        c                                            -                                              sin                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                                                  t                          ·                                                      xe2x80x83                                                    ⁢                          cos                                                ⁢                                                  xe2x80x83                                                ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                                                  t                          ·                          I                                                ⁢                                                  xe2x80x83                                                ⁢                        w                        ⁢                                                  xe2x80x83                                                ⁢                        d                        ⁢                                                  xe2x80x83                                                ⁢                        c                                                              )                                    ⁢                                      xe2x80x83                                    ⁢                                      ⅆ                    t                                                                                                                          =                              xe2x80x83                            ⁢                                                K                  ⁢                                                            3                      ⁢                                              3                                            ⁢                      Δ1                                        2                                    ⁢                                                            ∫                      0                                                                        2                          ⁢                          π                                                ω                                                              ⁢                                                                  (                                                                                                                                            1                                -                                                                  cos                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  4                                  ⁢                                  ω                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  t                                                                                            2                                                        ⁢                            cos                            ⁢                                                          xe2x80x83                                                        ⁢                            2                            ⁢                            θ                                                    -                                                                                                                    sin                                ⁢                                                                  xe2x80x83                                                                ⁢                                4                                ⁢                                ω                                ⁢                                                                  xe2x80x83                                                                ⁢                                t                                                            2                                                        ⁢                            sin                            ⁢                                                          xe2x80x83                                                        ⁢                            2                            ⁢                            θ                                                                          )                                            ⁢                                              ⅆ                        t                                                                                            +                                                                                                        xe2x80x83                            ⁢                                                ∫                  0                                                            2                      ⁢                      π                                        ω                                                  ⁢                                  (                                                                                                                                          sin                            ⁡                                                          (                                                                                                3                                  ⁢                                  ω                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  t                                                                +                                                                                                      2                                    3                                                                    ⁢                                  π                                                                                            )                                                                                +                                                      sin                            ⁡                                                          (                                                                                                ω                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  t                                                                -                                                                                                      2                                    3                                                                    ⁢                                  π                                                                                            )                                                                                                      2                                            ⁢                      I                      ⁢                                              xe2x80x83                                            ⁢                      u                      ⁢                                              xe2x80x83                                            ⁢                      d                      ⁢                                              xe2x80x83                                            ⁢                      c                                        -                                                                                                                                                            xe2x80x83                                ⁢                                                                                                                              sin                          ⁢                                                      xe2x80x83                                                    ⁢                          3                          ⁢                                                      xe2x80x83                                                    ⁢                          ω                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                +                                                  sin                          ⁢                                                      xe2x80x83                                                    ⁢                          ω                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                                    2                                        ⁢                    I                    ⁢                                          xe2x80x83                                        ⁢                    w                    ⁢                                          xe2x80x83                                        ⁢                    d                    ⁢                                          xe2x80x83                                        ⁢                    c                                    )                                            ⁢                              ⅆ                t                                                                                        =                              xe2x80x83                            ⁢                                                                    2                    ⁢                    π                                    ω                                ⁢                K                ⁢                                                      3                    ⁢                                          3                                        ⁢                    Δ1                                    4                                ⁢                cos                ⁢                                  xe2x80x83                                ⁢                2                ⁢                θ                                                                        (        22        )            
Therefore, the reference value extracting means can calculate the sine reference value and the cosine reference value by calculating the equations (21), (22) as the integrating process.
The rotor angle of the DC brushless motor can be calculated according to the following equation (23) from the sine reference value (Vs) calculated according to the equation (21) and the cosine reference value (Vc) calculated according to the equation (22):                     θ        =                              1            2                    ⁢                      tan                          -              1                                ⁢                      Vs                          V              ⁢                              xe2x80x83                            ⁢              c                                                          (        23        )            
The tanxe2x88x921 function varies greatly as the sine reference value (Vs) and the cosine reference value (Vc) vary. Therefore, when the rotor angle of the DC brushless motor is calculated according to the equation (23), a detecting error of the rotor angle may increase due to a calculating error of the sine reference value (Vs) and the cosine reference value (Vc).
In view of the foregoing shortcoming, the rotor angle calculating means generates phase difference data representing a phase difference (xcex8xe2x88x92{circumflex over (xcex8)}) between an estimated value ({circumflex over (xcex8)}) and an actual value (xcex8) of the rotor angle of the DC brushless motor according to the following equation (24) while the high-frequency voltages are imposed on the drive voltages by the high-frequency voltage imposing means and the sine reference value and the cosine reference value are extracted by the reference value extracting means in each control cycle, calculates the rotor angle of the DC brushless motor according to the above equation (23) in a first control cycle, and, in next and following control cycles, uses the rotor angle of the DC brushless motor calculated in a preceding control cycle as an estimated value ({circumflex over (xcex8)}) for the rotor angle of the DC brushless motor in the preceding control cycle, updates the estimated value ({circumflex over (xcex8)}) for the rotor angle of the DC brushless motor with an observer which sequentially updates and calculates the estimated value ({circumflex over (xcex8)}) for the rotor angle of the DC brushless motor based on the phase difference data to eliminate the phase difference (xcex8xe2x88x92{circumflex over (xcex8)}) depending on the phase difference data calculated in the preceding control cycle, thereby to calculate an estimated value ({circumflex over (xcex8)}) for the rotor angle of the DC brushless motor in a present control cycle, and uses the estimated value ({circumflex over (xcex8)}) for the rotor angle as the rotor angle of the DC brushless motor.                                                                                           V                  ⁢                                      xe2x80x83                                    ⁢                                      s                    ·                    cos                                    ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                                      θ                    ^                                                  -                                  V                  ⁢                                      xe2x80x83                                    ⁢                                      c                    ·                    sin                                    ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                                      θ                    ^                                                              ⁢                              xe2x80x83                            =                                                                                          V                      ⁢                                              xe2x80x83                                            ⁢                                              s                        2                                                              -                                          V                      ⁢                                              xe2x80x83                                            ⁢                                              c                        2                                                                                            ⁢                                  sin                  ⁡                                      (                                                                  2                        ⁢                        θ                                            -                                              2                        ⁢                                                  θ                          ^                                                                                      )                                                                                                                                          xe2x80x83                            ⁢                              ≈                                                                                                                              V                          ⁢                                                      xe2x80x83                                                    ⁢                                                      s                            2                                                                          -                                                  V                          ⁢                                                      xe2x80x83                                                    ⁢                                                      c                            2                                                                                                                ·                    2                                    ⁢                                      (                                          θ                      -                                              θ                        ^                                                              )                                                                                                                                          xe2x80x83                            ⁢                              (                                                                            in                      ⁢                                              xe2x80x83                                            ⁢                      c                      ⁢                                              xe2x80x83                                            ⁢                      a                      ⁢                                              xe2x80x83                                            ⁢                      s                      ⁢                                              xe2x80x83                                            ⁢                      e                      ⁢                                              xe2x80x83                                            ⁢                      θ                                        -                                          θ                      ^                                                        ≈                  0                                )                                                                        (        24        )            
With the above arrangement, the rotor angle calculating means calculates the rotor angle of the DC brushless motor according to the equation (23) only in the first control cycle. In next and following control cycles, the rotor angle calculating means applies the phase difference data generated based on the equation (24) in the preceding control cycle and the rotor angle of the DC brushless motor calculated in the preceding control cycle to the observer, and calculates an estimated value ({circumflex over (xcex8)}) for the rotor angle of the DC brushless motor in the preceding control cycle. The rotor angle calculating means can thus detect accurately the rotor angle of the DC brushless motor in the next and following control cycles.
The rotor angle calculating means uses, as the phase difference data, xcex94xcex81 produced by dividing the phase difference by {square root over (Vs2+Vc2)} according to the following equation (25) thereby to prevent the gain of the observer from varying depending on changes in the magnitudes of the sine reference value Vs and the cosine reference value Vc. Therefore, the rotor angle of the DC brushless motor can stably be detected.                                                                         Δθ                1                            =                                                2                  ⁢                                      (                                          θ                      -                                              θ                        ^                                                              )                                                  ≈                                  xe2x80x83                                ⁢                                  sin                  ⁡                                      (                                                                  2                        ⁢                        θ                                            -                                              2                        ⁢                                                  θ                          ^                                                                                      )                                                                                                                          =                              xe2x80x83                            ⁢                                                                    V                    ⁢                                          xe2x80x83                                        ⁢                                          s                      ·                      cos                                        ⁢                                          xe2x80x83                                        ⁢                    2                    ⁢                                          θ                      ^                                                        -                                      V                    ⁢                                          xe2x80x83                                        ⁢                                          c                      ·                      sin                                        ⁢                                          xe2x80x83                                        ⁢                    2                    ⁢                                          θ                      ^                                                                                                                                  V                      ⁢                                              xe2x80x83                                            ⁢                                              s                        2                                                              +                                          V                      ⁢                                              xe2x80x83                                            ⁢                                              c                        2                                                                                                                                                    (        25        )            
where xcex94xcex81: the phase difference data.
If the rotor angle calculating means has a relatively low calculating capability, the phase difference data xcex94xcex81 may be calculated by approximating calculations according to the following equation (26) instead of the equation (25):                                                                         Δθ                1                            =                                                2                  ⁢                                      (                                          θ                      -                                              θ                        ^                                                              )                                                  ≈                                  xe2x80x83                                ⁢                                  sin                  ⁡                                      (                                                                  2                        ⁢                        θ                                            -                                              2                        ⁢                                                  θ                          ^                                                                                      )                                                                                                                          ≈                              xe2x80x83                            ⁢                              {                                                                                                                                                                                        V                              ⁢                                                              xe2x80x83                                                            ⁢                                                              s                                ·                                cos                                                            ⁢                                                              xe2x80x83                                                            ⁢                              2                              ⁢                                                              θ                                ^                                                                                      -                                                          V                              ⁢                                                              xe2x80x83                                                            ⁢                                                              c                                ·                                sin                                                            ⁢                                                              xe2x80x83                                                            ⁢                              2                              ⁢                                                              θ                                ^                                                                                                                                          "LeftBracketingBar"                                                          V                              ⁢                                                              xe2x80x83                                                            ⁢                              s                                                        "RightBracketingBar"                                                                          ⁢                                                  xe2x80x83                                                ⁢                                                  (                                                                                    "LeftBracketingBar"                                                              V                                ⁢                                                                  xe2x80x83                                                                ⁢                                s                                                            "RightBracketingBar"                                                         greater than                                                           "LeftBracketingBar"                                                              V                                ⁢                                                                  xe2x80x83                                                                ⁢                                c                                                            "RightBracketingBar"                                                                                )                                                                                                                                                                                                                                                            V                              ⁢                                                              xe2x80x83                                                            ⁢                                                              s                                ·                                cos                                                            ⁢                                                              xe2x80x83                                                            ⁢                              2                              ⁢                                                              θ                                ^                                                                                      -                                                          V                              ⁢                                                              xe2x80x83                                                            ⁢                                                              c                                ·                                sin                                                            ⁢                                                              xe2x80x83                                                            ⁢                              2                              ⁢                                                              θ                                ^                                                                                                                                          "LeftBracketingBar"                                                          V                              ⁢                                                              xe2x80x83                                                            ⁢                              c                                                        "RightBracketingBar"                                                                          ⁢                                                  xe2x80x83                                                ⁢                                                  (                                                                                    "LeftBracketingBar"                                                              V                                ⁢                                                                  xe2x80x83                                                                ⁢                                c                                                            "RightBracketingBar"                                                         greater than                                                           "LeftBracketingBar"                                                              V                                ⁢                                                                  xe2x80x83                                                                ⁢                                s                                                            "RightBracketingBar"                                                                                )                                                                                                                                                                            (        26        )            
When the rotor angle of the DC brushless motor is detected according to the observer using the phase difference data xcex94xcex81 calculated according to the equation (25) and the phases of the currents supplied to the armatures of the DC brushless motor based on the detected rotor angle, a bottom value of the output torque of the DC brushless motor in a high current range, i.e., a lower end value of the varying range of the output torque, may be lowered, tending to increase the pulsation of the output torque. The inventors of the present invention have made various studies in order to suppress such a reduction in the bottom value of the output torque, and have found as a result that the bottom value of the output torque can be increased by forcibly shifting the rotor angle of the DC brushless motor calculated by the rotor angle calculating means to change the phase difference between the detected and actual values of the rotor angle.
The rotor angle calculating means can construct the observer using xcex94xcex82 calculated according to the following equation (27) with an offset value (offset) added thereto as the phase difference data, for thereby calculating the rotor angle of the DC brushless motor to equalize the difference between the detected and actual values of the rotor angle to the offset value. Thus, the phase difference between the detected and actual values of the rotor angle is forcibly shifted to suppress a reduction in the bottom value of the output torque for thereby reducing the pulsation of the output torque:                                                                         Δθ                2                            =                                                                    2                    ⁢                                          (                                              θ                        -                                                  θ                          ^                                                                    )                                                        +                  offset                                ≈                                  xe2x80x83                                ⁢                                                      sin                    ⁡                                          (                                                                        2                          ⁢                          θ                                                -                                                  2                          ⁢                                                      θ                            ^                                                                                              )                                                        +                  offset                                                                                                        =                              xe2x80x83                            ⁢                                                                                          V                      ⁢                                              xe2x80x83                                            ⁢                                              s                        ·                        cos                                            ⁢                                              xe2x80x83                                            ⁢                      2                      ⁢                                              θ                        ^                                                              -                                          V                      ⁢                                              xe2x80x83                                            ⁢                                              c                        ·                        sin                                            ⁢                                              xe2x80x83                                            ⁢                      2                      ⁢                                              θ                        ^                                                                                                                                                V                        ⁢                                                  xe2x80x83                                                ⁢                                                  s                          2                                                                    +                                              V                        ⁢                                                  xe2x80x83                                                ⁢                                                  c                          2                                                                                                                    +                offset                                                                        (        27        )            
where xcex94xcex82: the phase difference data.
The inductance of the rotor of the DC brushless motor varies in periodic cycles each having an electric angle of 180xc2x0. If the rotor angle of the DC brushless motor is detected by imposing the high-frequency voltages to the drive voltages of the DC brushless motor with the high-frequency voltage imposing means, then the direction of the magnetic poles of the rotor magnet of the DC brushless motor cannot be determined. That is, the rotor angle xcex8 (0xe2x89xa6xcex8xe2x89xa6180xc2x0) and the rotor angle xcex8+180xc2x0 cannot be detected separately from each other.
To overcome the above shortcoming, the inventors have made various studies and found that if the DC brushless motor is controlled according to a dq conversion process which handles the DC brushless motor as an equivalent circuit having a q-axis armature disposed on a q-axis extending in the direction of magnetic fluxes of field magnetic poles of the rotor of the DC brushless motor and a d-axis armature disposed on a d-axis extending perpendicularly to the q-axis, then when a current is passed through the q-axis armature and the rotor angle of the rotor is detected by the rotor angle calculating means, the sine reference value and the cosine reference value depending on the calculated rotor angle differ when the direction of the magnetic field generated by q-axis armature and the direction of the magnetic field generated by the magnetic poles of the rotor are the same as each other and when these directions are different from each other.
According to the present invention, the rotor angle detecting apparatus further includes correlation data storage means for handling the DC brushless motor as an equivalent circuit having a q-axis armature disposed on a q-axis extending in the direction of magnetic fluxes of field magnetic poles of the rotor of the DC brushless motor and a d-axis armature disposed on a d-axis extending perpendicularly to the q-axis, and storing, in advance, data of a map or a relational equation representing a correlation between a rotor angle of the DC brushless motor which is calculated by the rotor angle calculating means while a predetermined magnetic pole determining current is passed through the q-axis armature, and a threshold established between a saturated reference value which is calculated by a predetermined calculating process depending on the sine reference value and the cosine reference value which are extracted by the reference value extracting means when the rotor is in a saturated state in which the direction of a magnetic field generated by the q-axis armature and the direction of a magnetic field generated by magnetic poles of the rotor are the same as each other when the rotor angle is calculated, and an unsaturated reference value which is calculated by the predetermined calculating process depending on the sine reference value and the cosine reference value which are extracted by the reference value extracting means when the rotor is in an unsaturated state in which the direction of the magnetic field generated by the q-axis armature and the direction of the magnetic field generated by the magnetic poles of the rotor are opposite to each other when the rotor angle is calculated.
The rotor angle detecting apparatus also has magnetic pole direction determining means for handling the DC brushless motor as the equivalent circuit, and comparing a threshold value depending on the rotor angle which is obtained when the rotor angle calculated by the rotor angle calculating means while the magnetic pole determining current is passed through the q-axis armature is applied to the map or the relational equation, with a magnetic pole determining value calculated according to the predetermined calculating process depending on the sine reference value and the cosine reference value which are extracted by the reference value extracting means when the rotor angle is calculated, thereby to determine whether the rotor is in the saturated state or the unsaturated state for determining the direction of the magnetic poles of the rotor.
With the above arrangement, as described in greater detail later on, the magnetic pole direction determining means detects the rotor angle of the DC brushless motor while the magnetic pole determining current is passed through the q-axis armature. The magnetic pole direction determining means then compares a threshold value obtained by applying the calculated rotor angle to the map/relational equation with a magnetic pole determining value calculated according to the predetermined calculating process depending on the sine reference value and the cosine reference value which are extracted by the reference value extracting means when the rotor angle is calculated, thereby to determine the direction of the magnetic poles of the rotor. In this manner, the rotor angle of the DC brushless motor can be detected in a range from 0 to 360xc2x0.
The above and other objects, features, and advantages of the present invention will become apparent from the following description when taken in conjunction with the accompanying drawings which illustrate a preferred embodiment of the present invention by way of example.